Geometry on string lattice

TL;DR

This paper investigates the effective geometry of a two-dimensional string lattice using low energy modes, revealing symmetry properties and the relation to underlying lattice variables, with implications for supersymmetry breaking.

Contribution

It applies a method to derive the effective geometry on a string lattice and links it to lattice variables, extending understanding of low energy string dynamics.

Findings

Effective geometry is identical for tangent and transverse modes.

The low energy theory reduces to a 10D N=1 Maxwell theory.

Half of the supersymmetries are broken at high energy.

Abstract

Using the method developed by Callan and Thorlacius, we study the low energy effective geometry on a two-dimensional string lattice by examining the energy-momentum relations of the low energy propagation modes on the lattice. We show that the geometry is identical for both the oscillation modes tangent and transverse to the network plane. We determine the relation between the geometry and the lattice variables. The lowest order effective field theory is given by the dimensional reduction of the ten-dimensional N=1 Maxwell theory. The gauge symmetry is related to a property of a three-string junction but not of a higher order junction. A half of the supersymmetries in the effective field theory should be broken at high energy.